Spherical coordinates are a natural orthogonal system to describe wavefronts emanating from a point source. While a regular grid distribution in the Cartesian coordinate system tends to undersample the wavefront description near the source (the highest wavefront curvature) and oversample it away from the source, spherical coordinates, in general, provide a more balanced grid distribution to cha...

The present article outlines an innovative derivation of the well-known CRS traveltime formula. This is made possible by approximating the isochrones tangent to a small reflecting element embedded in a 3D homogeneous auxiliary medium. The arising paraxial traveltime formula is then parametrised by six attributes, each one characterising geometrically the wavefront of the reference normal-incide...

In this paper we present the program AMTCLAB, a MATLAB-based computer code that analyzes the traveltime distribution and performs quality analysis at the pre-inversion stage for elliptically anisotropic media explored via 2D transmission experiments. This software generalizes the program MTCLAB presented in the past for the case of layered isotropic media, and makes use of traditional and robus...

This paper presents a new traveltime inversion method based on the wave equation. In this new method, designated as wave-equation traveltime inversion (WT), seismograms are computed by any full-wave forward modeling method (we use a finitedifference method). The velocity model is perturbed until the traveltimes from the synthetic seismograms are best fitted to the observed traveltimes in a leas...

Seismic imaging, popularly known as tomography, borrowing the term from medical sciences, produces the raster image of the internal structure by combining information from a set of projections obtained at different viewing angles. To engineer high resolution and accurate solutions to mining problems, seismic traveltime tomography can yield a high resolution image of the subsurface to provide in...

In this work an adaptive strategy for the phase space method [5] for traveltime tomography is developed. The method uses those geodesics/rays that produces smaller mismatch with the measurements first and continue on in the spirit of layer stripping without the need to specifically defining the layers physically. The adaptive approach improves stability, efficiency and accuracy. We then extend ...

Fermat's principle shows that a deenite convex set of feasible slowness models { depending only on the traveltime data { exists for the fully nonlinear traveltime inversion problem. In a new iterative reconstruction algorithm, the minimum number of nonfeasible ray paths is used as a gure of merit to determine the optimum size of the model correction at each step. The numerical results show that...

The rst arrival quasi-P wave traveltime eld in an anisotropic elastic solid solves a rst order nonlinear partial diierential equation, the qP eikonal equation. Since the qP slowness surface is convex, the rst arrival traveltime along downward propagating rays solves the paraxial qP eikonal equation, an evolution equation in depth. A second order upwind nite diierence scheme solves this paraxial...